00000cam a22000003a 4500 UP-1685594773861907322 Buklod 20130220095023.0 g||| | || || ta 130220s2011 xx d r |||| u| 9780387721767 (hbk.) (iLib)UPBAG-00009830705 QA 241 B56 2011 Bloch, Ethan D. 1956- The real numbers and real analysis Ethan D. Bloch. New York Springer 2011. xxviii, 553 p. ill. 24 cm. Includes bibliographical references (p. 539-543) and index. Construction of the real numbers: Introduction ' Entry 1 : Axioms for the natural numbers ; Constructing the rational the integers ; Entry 1: Axioms for the integers ; Constructing the rational numbers ; Dedekind cuts ; Constructing the real numbers ; Historical remarks -- Properties of the real numbers: Introduction ; Entry 3: Axioms for the real numbers ; Algebraic properties of the real numbers ; Finding the natural numbers, the integers and the rational numbers in real numbers ; Induction and recursion in practice ; The least upper bound property and its consequences ; Uniqueness of the real numbers ; Decimal expansion of real numbers ; Historical remarks -- Limits and continuity: Introduction ; Limits of functions ; Continuity ; Uniform continuity ; Two important theorems ; Historical remarks -- Differentiation: Introduction ; The derivative ; Computing derivatives ; The mean value theorem ; increasing and decreasing functions, Part 1: Local and global extrema ; Increasing and decreasing functions, Part II: Further topics ; Historical remarks -- Integration: Introduction ; The Riemann integral ; Elementary properties of the Riemann integral ; Upper sums and lower sums ; Further properties of the Riemann integral ; Fundamental theorem of calculus ; Computing antiderivatives ; Lebesgue's theorem ; Area and arc length ; Historical remarks -- Limits to infinity: Introduction ; Limits to infinity ; Computing limits to infinity ; Improper integrals ; Historical remarks -- Transcendental functions: Introduction ; Logarithmic and exponential functions ; Trigonometric functions ; More about [Pi] ; Historical remarks -- Sequences: Introduction ; Sequences ; Three important theorems ; applications of sequences ; Historical remarks -- Series: Introduction ; Series ; Convergence tests ; Absolute convergence and conditional convergence ; Power series as functions ; Historical remarks -- Sequences and series of functions: Introduction ; Sequences of functions ; Series of functions ; Functions as power series ; A continuous but nowhere differentiable function ; Historical remarks. Numbers, Real. UPBAG UPBAG-MAIN QA 241 B56 2011 Book